A novel viscoplastic model for salt rock deformation under internal cyclic gas pressure loading

Abstract

Salt caverns are widely used for energy storage. During gas storage, the internal gas pressure fluctuates cyclically in response to energy demand, making it essential to assess how these pressure variations affect rock deformation. In this study, experiments were conducted under different cyclic gas pressure conditions to investigate this effect. The findings indicate that (1) the deformation process of salt rock can be segmented into three stages: the deceleration stage, the steady-state stage, and the acceleration stage. (2) When the axial pressure remains constant, both axial and radial deformations exhibit a stepwise increasing trend in response to cyclic gas pressure variations. Similarly, under axial graded loading, the deformations also demonstrate a progressive rise. By analyzing the deformation differences and model coefficient fluctuations within a single gas pressure cycle, it is found that radial deformation is higher sensitive to changes in cyclic gas pressure. (3) The axial deformation shows a stepwise increase, and the radial deformation showed a cyclic change with changing gas pressure. Therefore, the cyclic gas pressure influence factor α, axial loading influence factor β, and state variable σ∗ are introduced to develop a viscoplastic ontological model that accounts for the impacts of cyclic gas pressure, confining pressure and axial stress. Validated by the deformation data, the new model can better fit both the axial deformation and the radial deformation of the three stages and has strong applicability and accuracy by changing only fewer parameters. The state variable rate shows the same stage as the deformation rate and residual strain of salt rock, which can better reflect the internal hardening of salt rock.

Keywords

Salt rock / Gas pressure / Effective stress / Residual strain / Viscoplastic model

Acknowledgments

This work was supported by the National Natural Science Foun-dation of China (No. 52274073), National Key R&D Program of China (No. 2024YFB4007100), Chongqing Natural Science Founda-tion Innovation and Development Joint Fund (Municipal Education Commission) (No. CSTB2024NSCQ-LZX0056), and Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Safety (No. SKLGGES-024006). The authors are also grateful for the financial support from the Rut and Sten Brand Foundation.

References

[1] Li ZZ, Kang YF, Fan JY, Fourmeau M, Chen J, Jiang DY, Nelias D. Macroscopic experimental study and microscopic phenomenon analysis of damage self-healing in salt rock. Eng Geol 2024; 338:107634.

[2] Tang LX, Fan JY, Li ZZ, Chen J, Liu W. A new constitutive model for salt rock under cyclic loadings based on state variables. Geoenergy Sci Eng 2024; 233:212433.

[3] Wang JB, Liu X, Zhang Q, Liu XR, Song ZP, Feng SJ. Fatigue properties and damage constitutive model of salt rock based on CT scanning. Int J Min Sci Technol 2024; 34(2):245-59.

[4] Fan JY, Xie HP, Chen J, Jiang DY, Li CB, Ngaha Tiedeu W, Ambre J. Preliminary feasibility analysis of a hybrid pumped-hydro energy storage system using abandoned coal mine goafs. Appl Energy 2020; 258:114007.

[5] Xie YC, Luo JS, Hou ZM, Li GS, Liu JH, Tang JW, Huang LC, Beck HP, Yang CH. Large-scale underground storage of renewable energy coupled with power-to-X: Challenges, trends, and potentials in China. Engineering 2023; 29:15-21.

[6] Sedaee B, Mohammadi M, Esfahanizadeh L, Fathi Y. Comprehensive modeling and developing a software for salt cavern underground gas storage. J. Energy Storage 2019; 25:100876.

[7] Saeed M, Jadhawar P. Modelling underground hydrogen storage: A state-of-the-art review of fundamental approaches and findings. Gas Sci Eng 2024; 121:205196.

[8] Aneke M, Wang MH. Energy storage technologies and real life applications: A state of the art review. Appl Energy 2016; 179:350-77.

[9] Chu LK, Ghosh S, Dog˘an B, Nguyen NH, Shahbaz M. Energy security as new determinant of renewable energy: The role of economic complexity in top energy users. Energy 2023; 263:125799.

[10] Sovacool BK, Mukherjee I. Conceptualizing and measuring energy security: A synthesized approach. Energy 2011; 36(8):5343-55.

[11] Wang YF, Zhang X, Jiang DY, Liu W, Wan JF, Li ZY, Fan JY, Wang WH. Study on stability and economic evaluation of two-well-vertical salt cavern energy storage. J. Energy Storage 2022; 56:106164.

[12] Liu W, Li QH, Yang CH, Shi XL, Wan JF, Jurado MJ, Li YP, Jiang DY, Chen J, Qiao WB, Zhang X, Fan JY, Peng TJ, He YX. The role of underground salt caverns for large-scale energy storage: A review and prospects. Energy Storage Mater 2023; 63:103045.

[13] Wang JK, Wu R, Wei MZ, Bai BJ, Xie J, Li YH. A comprehensive review of site selection, experiment and numerical simulation for underground hydrogen storage. Gas Sci Eng 2023; 118:205105.

[14] Safaei H, Keith DW, Hugo RJ. Compressed air energy storage (CAES) with compressors distributed at heat loads to enable waste heat utilization. Appl Energy 2013; 103:165-79.

[15] He QC, Liu JF, Wu F, Li CB, Chen J, Gao RB, Ye CF, Zhu SJ. Fatigue properties and constitutive model of Jintan salt rock subjected to complex cyclic loading. Int J Min Sci Technol 2025; 35(1):121-33.

[16] Chen XS, Xiong TK, Li YP. Research on the helium seepage mechanism in the strata surrounding bedded salt cavern helium storage and its tightness evaluation. Geoenergy Sci Eng 2024; 238:212870.

[17] Mwakipunda GC, Mgimba MM, Ngata MR, Yu L. Recent advances on carbon dioxide sequestration potentiality in salt caverns: A review. Int. J. Greenh. Gas Contr. 2024; 133:104109.

[18] Fan JY, Jiang DY, Liu W, Wu F, Chen J, Daemen J. Discontinuous fatigue of salt rock with low-stress intervals. Int J Rock Mech Min Sci 2019; 115:77-86.

[19] Pouya A, Zhu C, Arson C. Micro-macro approach of salt viscous fatigue under cyclic loading. Mech Mater 2016; 93:13-31.

[20] Grgic D, Al Sahyouni F, Golfier F, Moumni M, Schoumacker L. Evolution of gas permeability of rock salt under different loading conditions and implications on the underground hydrogen storage in salt caverns. Rock Mech Rock Eng 2022; 55(2):691-714.

[21] Lyu C, Liu JF, Ren Y, Liang C, Zeng Y. Mechanical characteristics and permeability evolution of salt rock under thermal-hydro-mechanical (THM) coupling condition. Eng Geol 2022; 302:106633.

[22] Peng HH, Fan JY, Zhang X, Chen J, Li ZZ, Jiang DY, Liu C. Computed tomography analysis on cyclic fatigue and damage properties of rock salt under gas pressure. Int J Fatigue 2020; 134:105523.

[23] Damasceno DR, Spross J, Johansson F. Rock mass response for lined rock caverns subjected to high internal gas pressure. J Rock Mech Geotech Eng 2023; 15(1):119-29.

[24] Liu W, Liu WH, Fan JY, Chen J. Relaxation test and constitutive model of salt rock under the coupled effect of stress and air pressure. J. Energy Storage 2025; 115:115930.

[25] Li P, Kang H, Zhu Q, Wu Y, Zhang J, Fan LY, Wang Z. Numerical and experimental investigations of concrete lined compressed air energy storage system. J Clean Prod 2023; 390:136153.

[26] Miao ST, Pan PZ, Cao YB, Huo L. Enhancing understanding of fracture mechanisms in brittle rocks under static and cyclic loads: Experimental insights and theoretical model. Eng Fract Mech 2023; 289:109426.

[27] Fourmeau M, Liu W, Li ZZ, Nelias D, Fan JY, Tian H, Liu W. Research status of creep-fatigue characteristics of salt rocks and stability of compressed air storage in salt caverns. Earth Energy Sci 2025; 1:98-116.

[28] Zhou HW, Wang CP, Han BB, Duan ZQ. A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 2011; 48(1):116-21.

[29] Ulusay R. The present and future of rock testing:Highlighting the ISRM suggested methods. In: The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007-2014. Switzerland: Springer Cham; 2014.p. 1-22.

[30] Bieniawski ZT, Bernede MJ. Suggested methods for determining the uniaxial compressive strength and deformability of rock materials Part 1. Suggested method for determining deformability of rock materials in uniaxial compression. Int J Rock Mech Min Sci Geomech Abstr 1979; 16(2):138-40.

[31] Li ZZ, Kang YF, Fan JY, Fourmeau M, Jiang DY, Nelias D. Creep-fatigue mechanical characteristics of salt rocks under triaxial loading: An experimental study. Eng Geol 2023; 322:107175.

[32] Li ZZ, Yang ZY, Fan JY, Fourmeau M, Jiang DY, Nelias D. Fatigue mechanical properties of salt rocks under high stress plateaus: The interaction between creep and fatigue. Rock Mech Rock Eng 2022; 55(11):6627-42.

[33] Urai JL, Spiers CJ, Zwart HJ, Lister GS. Weakening of rock salt by water during long-term creep. Nature 1986; 324(6097):554-7.

[34] Le Comte P. Creep in rock salt. J Geol 1965; 73(3):469-84.

[35] Senseny PE, Hansen FD, Russell JE, Carter NL, Handin JW. Mechanical behaviour of rock salt: Phenomenology and micromechanisms. Int J Rock Mech Min Sci Geomech Abstr 1992; 29(4):363-78.

[36] Mansouri H, Ajalloeian R. Mechanical behavior of salt rock under uniaxial compression and creep tests. Int J Rock Mech Min Sci 2018; 110:19-27.

[37] Skrotzki W, Haasen P. Plastic deformation and hardening of polycrystalline halides. In:Deformation of Ceramic Materials II. Boston: Springer US; 1984. p. 429-44.

[38] Yang F, Fan JY, Yang ZY, Liu W, Chen J. Plasticity analysis and constitutive model of salt rock under different loading speeds. J. Energy Storage 2023; 67:107583.

[39] Wang CP, Liu JF, Chen L, Liu J, Wang L, Liao YL. Creep constitutive model considering nonlinear creep degradation of fractured rock. Int J Min Sci Technol 2024; 34(1):105-16.

[40] Fan JY, Chen J, Jiang DY, Chemenda A, Chen JC, Ambre J.Discontinuous cyclic loading tests of salt with acoustic emission monitoring. Int J Fatigue 2017; 94:140-4.

[41] Jiang DY, Fan JY, Chen J, Li L, Cui Y. A mechanism of fatigue in salt under discontinuous cycle loading. Int J Rock Mech Min Sci 2016; 86:255-60.

[42] Sattar M, Othman AR, Kamaruddin S, Akhtar M, Khan R. Limitations on the computational analysis of creep failure models: A review. Eng Fail Anal 2022; 134:105968.

[43] Firme PALP, Brandao NB, Roehl D, Romanel C. Enhanced double-mechanism creep laws for salt rocks. Acta Geotech 2018; 13(6):1329-40.

[44] Maheshwari P. Analysis of deformation of linear viscoelastic two layered laminated rocks. Int J Rock Mech Min Sci 2021; 141:104681.

[45] Nomikos P, Rahmannejad R, Sofianos A. Supported axisymmetric tunnels within linear viscoelastic burgers rocks. Rock Mech Rock Eng 2011; 44 (5):553-64.

[46] Chen YA, Zhao GM, Xu WS, Peng SJ, Xu J. Development and application of rock rheological constitutive model considering dynamic stress field and seepage field. Int J Min Sci Technol 2025; 35(3):467-82.

[47] Gao RB, Wu F, Chen J, Zhu C, Ji CX. Study on creep characteristics and constitutive model of typical argillaceous salt rock in energy storage caverns in China. J. Energy Storage 2022; 50:104248.